A production line has two machines, Machine A and Machine B, that are arranged in series. Each jol needs to processed by Machine A first. Once it finishes the processing by Machine A, it moves to the next station, to be processed by Machine B. Once it finishes the processing by Machine B, it leaves the production line. Each machine can process one job at a time. An arriving job that finds the machine busy waits in a buffer. (The buffer sizes are assumed to be infinite.) The processing times for Machine A are iid having exponential distribution with mean 4 minutes. The processing times for Machine B are iid with mean 2 minutes. Assume that the interarrival times of jobs arriving at the production line are iid, having exponential distribution with mean of 5 minutes (a) What is the utilization of Machine A? What is the utilization of Machine B?(b) What is the throughput of the production system?(c) What is the average waiting time at Machine A, excluding the service time?(d) It is known the average time in the entire production line is 30 minutes per job. What is the long-run average number of jobs in the entire production line?(e) Suppose that the mean interarrival time is changed to 1 minute. What are the utilizations for Machine A and Machine B, respectively? What is the throughput of the production system?

Look at arnold's attempt to solve the equation for b: 3b = 12 b = 3 · 12 b = 36 describe the mistake that arnold made.

If you are trying to move an attached term across the equal sign (=), what operation would you use to move it?

Airplane speeds are measured in three different ways: (1) indicated speed, (2) true speed, and (3) ground speed. the indicated airspeed is the airspeed given by an instrument called an airspeed indicator. a plane’s indicated airspeed is different from its true airspeed because the indicator is affected by temperature changes and different altitudes of air pressure. the true airspeed is the speed of the airplane relative to the wind. ground speed is the speed of the airplane relative to the ground. for example, a plane flying at a true airspeed of 150 knots into a headwind of 25 knots will have a ground speed of 125 knots. the problems below refer to static and dynamic pressure. static pressure is used when a body is in motion or at rest at a constant speed and direction. dynamic pressure is used when a body in motion changes speed or direction or both. a gauge compares these pressures, giving pilots an indicated airspeed. in problem #s 1 and 2, use the following information. the indicated airspeed s (in knots) of an airplane is given by an airspeed indicator that measures the difference p (in inches of mercury) between the static and dynamic pressures. the relationship between s and p can be modeled by s=136.4p√+4.5. 1. find the differential pressure when the indicated airspeed is 157 knots. 2. find the change in the differential pressure of an airplane that was traveling at 218 knots and slowed down to195 knots. in problem #s 3 and 4, use the following information. the true airspeed t (in knots) of an airplane can be modeled by t=(1+a50,000) ⋅ s, where a is the altitude (in feet) and s is the indicated airspeed (in knots). 3. write the equation for true airspeed t in terms of altitude and differential pressure p. 4. a plane is flying with a true airspeed of 280 knots at an altitude of 20,000 feet. estimate the differential pressure. explain why you think your estimate is correct.